A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. The plot shown in the figure indicates the one that represents the velocity \((v)\) of the pebble as a function of time \((t).\)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Hint: Use the concept of Stoke's law.
Step: Find the variation of velocity with time \(t.\)
The pebble is dropped with zero initial velocity. Initially, the pebble will accelerate downward due to gravity. As it moves through the viscous oil, it experiences a drag force that opposes its motion. This drag force increases with velocity and it is given by;
\(F=6\pi \eta r v\)
Eventually, the pebble will reach a constant velocity known as terminal velocity when the drag force equals the gravitational force acting on the pebble. Therefore, the graph given below represents the velocity \((v)\) of the pebble as a function of time \((t).\)
Hence, option (3) is the correct answer.
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